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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 133 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
186.2.a.a	$186$	$2$	186.a	1.a	$1$	$1$	$1$	$1.485$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots$
186.2.a.b	$186$	$2$	186.a	1.a	$1$	$1$	$1$	$1.485$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-2q^{7}+\cdots$
186.2.a.c	$186$	$2$	186.a	1.a	$1$	$1$	$1$	$1.485$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
186.2.a.d	$186$	$2$	186.a	1.a	$1$	$2$	$2$	$1.485$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$2$	$-2$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots$
186.2.c.a	$186$	$2$	186.c	93.c	$2$	$4$	$4$	$1.485$	$\Q(\zeta_{12})$	None		$4$	$0$	$0$	$0$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{12}q^{2}+\zeta_{12}^{3}q^{3}-q^{4}-3\zeta_{12}q^{5}+\cdots$
186.2.c.b	$186$	$2$	186.c	93.c	$2$	$8$	$8$	$1.485$	8.0.$\cdots$.8	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+\beta _{4}q^{3}-q^{4}+2\beta _{3}q^{5}+\beta _{5}q^{6}+\cdots$
186.2.e.a	$186$	$2$	186.e	31.c	$3$	$2$	$1$	$1.485$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$1$	$-2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(1-\zeta_{6})q^{3}+q^{4}-2\zeta_{6}q^{5}+\cdots$
186.2.e.b	$186$	$2$	186.e	31.c	$3$	$2$	$1$	$1.485$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$-1$	$2$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+2\zeta_{6}q^{5}+\cdots$
186.2.e.c	$186$	$2$	186.e	31.c	$3$	$4$	$2$	$1.485$	$\Q(\sqrt{-3}, \sqrt{19})$	None		$2$	$0$	$-4$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{2}+\cdots)q^{6}+\cdots$
186.2.e.d	$186$	$2$	186.e	31.c	$3$	$4$	$2$	$1.485$	$\Q(\sqrt{2}, \sqrt{-3})$	None		$2$	$0$	$4$	$2$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}-\beta _{2}q^{3}+q^{4}+2\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots$
186.2.f.a	$186$	$2$	186.f	31.d	$5$	$4$	$1$	$1.485$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$-1$	$2$	$7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+\cdots$
186.2.f.b	$186$	$2$	186.f	31.d	$5$	$4$	$1$	$1.485$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$1$	$-4$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+\cdots$
186.2.f.c	$186$	$2$	186.f	31.d	$5$	$8$	$2$	$1.485$	8.0.9240015625.1	None		$2$	$0$	$-2$	$2$	$2$	$-7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{3}q^{2}+\beta _{5}q^{3}+\beta _{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
186.2.h.a	$186$	$2$	186.h	93.g	$6$	$20$	$10$	$1.485$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$2$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{6}q^{2}+(-\beta _{9}-\beta _{14})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
186.2.j.a	$186$	$2$	186.j	93.k	$10$	$48$	$12$	$1.485$		None		$4$	$0$	$0$	$0$	$0$	$-18$			$\mathrm{SU}(2)[C_{10}]$
186.2.m.a	$186$	$2$	186.m	31.g	$15$	$8$	$1$	$1.485$	$\Q(\zeta_{15})$	None		$2$	$0$	$-2$	$1$	$3$	$-4$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+\zeta_{15}^{6}q^{2}+\zeta_{15}^{4}q^{3}+(-\zeta_{15}^{2}-\zeta_{15}^{7})q^{4}+\cdots$
186.2.m.b	$186$	$2$	186.m	31.g	$15$	$8$	$1$	$1.485$	$\Q(\zeta_{15})$	None		$2$	$0$	$2$	$-1$	$7$	$14$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q-\zeta_{15}^{6}q^{2}-\zeta_{15}^{4}q^{3}+(-\zeta_{15}^{2}-\zeta_{15}^{7})q^{4}+\cdots$
186.2.m.c	$186$	$2$	186.m	31.g	$15$	$8$	$1$	$1.485$	$\Q(\zeta_{15})$	None		$2$	$0$	$2$	$1$	$-5$	$2$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q-\zeta_{15}^{6}q^{2}+\zeta_{15}^{4}q^{3}+(-\zeta_{15}^{2}-\zeta_{15}^{7})q^{4}+\cdots$
186.2.m.d	$186$	$2$	186.m	31.g	$15$	$8$	$1$	$1.485$	$\Q(\zeta_{15})$	None		$2$	$0$	$2$	$1$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q-\zeta_{15}^{6}q^{2}+\zeta_{15}^{4}q^{3}+(-\zeta_{15}^{2}-\zeta_{15}^{7})q^{4}+\cdots$
186.2.m.e	$186$	$2$	186.m	31.g	$15$	$16$	$2$	$1.485$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$-4$	$-2$	$-5$	$-8$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(-1+\beta _{3}-\beta _{6}+\beta _{8}+\beta _{9}-\beta _{10}+\cdots)q^{2}+\cdots$
186.2.p.a	$186$	$2$	186.p	93.p	$30$	$80$	$10$	$1.485$		None		$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{30}]$
186.3.b.a	$186$	$3$	186.b	3.b	$2$	$20$	$20$	$5.068$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$0$	$4$	$0$	$0$		$2^{11}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}-\beta _{17}q^{3}-2q^{4}+\beta _{6}q^{5}+\cdots$
186.3.d.a	$186$	$3$	186.d	31.b	$2$	$12$	$12$	$5.068$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$8$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}-\beta _{2}q^{3}+2q^{4}+(\beta _{4}-\beta _{6}+\cdots)q^{5}+\cdots$
186.3.g.a	$186$	$3$	186.g	31.e	$6$	$8$	$4$	$5.068$	8.0.$\cdots$.2	None		$2$	$0$	$0$	$-12$	$0$	$-12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{5}q^{2}+(-2-\beta _{3})q^{3}+2q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
186.3.g.b	$186$	$3$	186.g	31.e	$6$	$12$	$6$	$5.068$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$18$	$0$	$8$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{2}q^{2}+(2+\beta _{1})q^{3}+2q^{4}+\beta _{4}q^{5}+\cdots$
186.3.i.a	$186$	$3$	186.i	93.h	$6$	$44$	$22$	$5.068$		None		$4$	$0$	$0$	$-4$	$0$	$8$			$\mathrm{SU}(2)[C_{6}]$
186.3.k.a	$186$	$3$	186.k	93.l	$10$	$80$	$20$	$5.068$		None		$4$	$0$	$0$	$-4$	$0$	$20$			$\mathrm{SU}(2)[C_{10}]$
186.3.l.a	$186$	$3$	186.l	31.f	$10$	$48$	$12$	$5.068$		None		$2$	$0$	$0$	$0$	$0$	$12$			$\mathrm{SU}(2)[C_{10}]$
186.3.n.a	$186$	$3$	186.n	31.h	$30$	$32$	$4$	$5.068$		None		$2$	$0$	$0$	$12$	$0$	$2$			$\mathrm{SU}(2)[C_{30}]$
186.3.n.b	$186$	$3$	186.n	31.h	$30$	$48$	$6$	$5.068$		None		$2$	$0$	$0$	$-18$	$0$	$-18$			$\mathrm{SU}(2)[C_{30}]$
186.3.o.a	$186$	$3$	186.o	93.o	$30$	$176$	$22$	$5.068$		None		$4$	$0$	$0$	$4$	$0$	$-28$			$\mathrm{SU}(2)[C_{30}]$
186.4.a.a	$186$	$4$	186.a	1.a	$1$	$1$	$1$	$10.974$	$\Q$	None	✓	$1$	$1$	$-2$	$-3$	$3$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+3q^{5}+6q^{6}+\cdots$
186.4.a.b	$186$	$4$	186.a	1.a	$1$	$1$	$1$	$10.974$	$\Q$	None	✓	$1$	$0$	$-2$	$3$	$-11$	$-22$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}-11q^{5}-6q^{6}+\cdots$
186.4.a.c	$186$	$4$	186.a	1.a	$1$	$1$	$1$	$10.974$	$\Q$	None	✓	$1$	$1$	$-2$	$3$	$-11$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}-11q^{5}-6q^{6}+\cdots$
186.4.a.d	$186$	$4$	186.a	1.a	$1$	$1$	$1$	$10.974$	$\Q$	None	✓	$1$	$0$	$-2$	$3$	$15$	$17$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}+15q^{5}-6q^{6}+\cdots$
186.4.a.e	$186$	$4$	186.a	1.a	$1$	$1$	$1$	$10.974$	$\Q$	None	✓	$1$	$1$	$2$	$-3$	$-7$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}-7q^{5}-6q^{6}+\cdots$
186.4.a.f	$186$	$4$	186.a	1.a	$1$	$1$	$1$	$10.974$	$\Q$	None	✓	$1$	$1$	$2$	$3$	$-21$	$-19$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}-21q^{5}+6q^{6}+\cdots$
186.4.a.g	$186$	$4$	186.a	1.a	$1$	$1$	$1$	$10.974$	$\Q$	None	✓	$1$	$0$	$2$	$3$	$-1$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}-q^{5}+6q^{6}+\cdots$
186.4.a.h	$186$	$4$	186.a	1.a	$1$	$2$	$2$	$10.974$	$\Q(\sqrt{97}) $	None	✓	$1$	$0$	$-4$	$-6$	$-2$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+(1-4\beta )q^{5}+\cdots$
186.4.a.i	$186$	$4$	186.a	1.a	$1$	$2$	$2$	$10.974$	$\Q(\sqrt{521}) $	None	✓	$1$	$0$	$4$	$6$	$15$	$29$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+(8-\beta )q^{5}+6q^{6}+\cdots$
186.4.a.j	$186$	$4$	186.a	1.a	$1$	$3$	$3$	$10.974$	3.3.148233.1	None	✓	$1$	$0$	$6$	$-9$	$8$	$11$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}+(2+\beta _{1}-\beta _{2})q^{5}+\cdots$
186.4.c.a	$186$	$4$	186.c	93.c	$2$	$32$	$32$	$10.974$		None		$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
186.4.e.a	$186$	$4$	186.e	31.c	$3$	$2$	$1$	$10.974$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-4$	$3$	$-10$	$-24$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2q^{2}+(3-3\zeta_{6})q^{3}+4q^{4}-10\zeta_{6}q^{5}+\cdots$
186.4.e.b	$186$	$4$	186.e	31.c	$3$	$6$	$3$	$10.974$	6.0.2517435072.1	None		$2$	$0$	$-12$	$9$	$-6$	$10$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-2q^{2}+3\beta _{1}q^{3}+4q^{4}+(-2+2\beta _{1}+\cdots)q^{5}+\cdots$
186.4.e.c	$186$	$4$	186.e	31.c	$3$	$6$	$3$	$10.974$	6.0.4956535827.1	None		$2$	$0$	$12$	$9$	$2$	$27$		$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	$q+2q^{2}+(3-3\beta _{3})q^{3}+4q^{4}+(\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$
186.4.e.d	$186$	$4$	186.e	31.c	$3$	$8$	$4$	$10.974$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$-16$	$-12$	$10$	$9$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-2q^{2}-3\beta _{4}q^{3}+4q^{4}+(2-2\beta _{4}+\cdots)q^{5}+\cdots$
186.4.e.e	$186$	$4$	186.e	31.c	$3$	$10$	$5$	$10.974$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$20$	$-15$	$4$	$-12$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+2q^{2}+3\beta _{2}q^{3}+4q^{4}+(1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
186.4.f.a	$186$	$4$	186.f	31.d	$5$	$12$	$3$	$10.974$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$6$	$-9$	$-18$	$21$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+2\beta _{2}q^{2}+3\beta _{7}q^{3}+4\beta _{4}q^{4}+(-1+\cdots)q^{5}+\cdots$
186.4.f.b	$186$	$4$	186.f	31.d	$5$	$16$	$4$	$10.974$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-8$	$-12$	$32$	$-14$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+2\beta _{4}q^{2}+3\beta _{5}q^{3}+4\beta _{6}q^{4}+(3-\beta _{3}+\cdots)q^{5}+\cdots$
186.4.f.c	$186$	$4$	186.f	31.d	$5$	$16$	$4$	$10.974$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-8$	$12$	$-26$	$67$		$2^{4}\cdot 3^{4}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q-2\beta _{1}q^{2}-3\beta _{3}q^{3}-4\beta _{4}q^{4}+(-2+\cdots)q^{5}+\cdots$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.